Constructing and sampling partite, 3-uniform hypergraphs with given degree sequence.

Partite, 3-uniform hypergraphs are 3-uniform hypergraphs in which each hyperedge contains exactly one point from each of the 3 disjoint vertex classes. We consider the degree sequence problem of partite, 3-uniform hypergraphs, that is, to decide if such a hypergraph with prescribed degree sequences exists. We prove that this decision problem is NP-complete in general, and give a polynomial running time algorithm for third almost-regular degree sequences, that is, when each degree in one of the vertex classes is k or k - 1 for some fixed k, and there is no restriction for the other two vertex classes. We also consider the sampling problem, that is, to uniformly sample partite, 3-uniform hypergraphs with prescribed degree sequences. We propose a Parallel Tempering method, where the hypothetical energy of the hypergraphs measures the deviation from the prescribed degree sequence. The method has been implemented and tested on synthetic and real data. It can also be applied for χ2 testing of contingency tables. We have shown that this hypergraph-based χ2 test is more sensitive than the standard χ2 test. The extra sensitivity is especially advantageous on small data sets, where the proposed Parallel Tempering method shows promising performance.

Do pathogens always evolve to be less virulent? The virulence-transmission trade-off in light of the COVID-19 pandemic.

The direction the evolution of virulence takes in connection with any pathogen is a long-standing question. Formerly, it was theorized that pathogens should always evolve to be less virulent. As observations were not in line with this theoretical outcome, new theories emerged, chief among them the transmission-virulence trade-off hypotheses, which predicts an intermediate level of virulence as the endpoint of evolution. At the moment, we are very much interested in the future evolution of COVID-19's virulence. Here, we show that the disease does not fulfill all the assumptions of the hypothesis. In the case of COVID-19, a higher viral load does not mean a higher risk of death; immunity is not long-lasting; other hosts can act as reservoirs for the virus; and death as a consequence of viral infection does not shorten the infectious period. Consequently, we cannot predict the short- or long-term evolution of the virulence of COVID-19.

Prevalence, epidemiology and associated healthcare burden of Rome IV irritable bowel syndrome and functional dyspepsia in the adult population of Gibraltar.

OBJECTIVE: Gibraltar is a unique densely populated multicultural British Overseas Territory for which no population data on disorders of gut-brain interaction have existed.We aimed to provide the first-ever assessment of prevalence of irritable bowel syndrome and functional dyspepsia in Gibraltar in relation to their diagnostic recognition and healthcare burden. DESIGN: An internet survey was carried out in Gibraltar in 2019-2020. The study survey included demographic questions, the Rome IV diagnostic questions for functional dyspepsia and irritable bowel syndrome, relevant medical history, previous surgeries, medication use, healthcare visit frequency and a quality-of-life questionnaire. RESULTS: 888 individuals (3.5% of all Gibraltar adults) completed the survey anonymously. Irritable bowel syndrome prevalence was 5.2% (95% CI 3.7% to 6.6%). Functional dyspepsia prevalence was 9.9% (95% CI 7.9% to 11.9%). The two conditions overlapped substantially. Women had higher mean prevalence than men of both disorders. People meeting criteria for either or both disorders were prone to surgeries, had more frequent healthcare visits, higher medication use and lower quality-of-life scores compared with people without these disorders. Diagnostic recognition by healthcare providers was low, leaving 58.3% of irritable bowel syndrome and 96.9% of functional dyspepsia individuals undiagnosed. CONCLUSION: This first-ever population-based study of Rome IV defined irritable bowel syndrome and functional dyspepsia in Gibraltar indicates that the prevalence rates of these disorders are similar to the recently reported data for the UK and Spain, but they remain poorly recognised despite substantially affecting the quality of life of individuals who have them in the Gibraltar community.

The plant in the labyrinth: Adaptive growth and branching in heterogeneous environments.

The "ant in the labyrinth" problem describes spatial constraints upon a moving agent in a disordered medium. In contrast with an animal-like agent (an "ant"), a clonal plant can stay in a place and move at the same time: some parts develop roots, while others continue moving by horizontal growth and branching. Hereby we present a spatially explicit, dynamic model for the study of percolation by plant growth rules in lattices that consist of open and closed sites. Growth always starts from a single seed in an open percolation cluster (patch). By increasing the proportion of open sites (p), we describe a new kind of threshold (the "tracking threshold", approximately pt=0.73), which is higher than the site percolation threshold (pc=0.5 in this lattice). At pc

Maximal gene number maintainable by stochastic correction - The second error threshold.

There is still no general solution to Eigen׳s Paradox, the chicken-or-egg problem of the origin of life: neither accurate copying, nor long genomes could have evolved without one another being established beforehand. But an array of small, individually replicating genes might offer a workaround, provided that multilevel selection assists the survival of the ensemble. There are two key difficulties that such a system has to overcome: the non-synchronous replication of genes, and their random assortment into daughter cells (the units of higher-level selection) upon fission. Here we find, using the Stochastic Corrector Model framework, that a large number (τ≥90) of genes can coexist. Furthermore, the system can tolerate about 10% replication rate asymmetry (competition) among the genes. On this basis, we put forward a plausible (and testable!) scenario for how novel genes could have been incorporated into early living systems: a route to complex metabolism.

Patch size and distance: modelling habitat structure from the perspective of clonal growth.

BACKGROUND AND AIMS: This study considers the spatial structure of patchy habitats from the perspective of plants that forage for resources by clonal growth. Modelling is used in order to compare two basic strategies, which differ in the response of the plant to a patch boundary. The 'avoiding plant' (A) never grows out of a good (resource-rich) patch into a bad (resource-poor) region, because the parent ramet withdraws its subsidy from the offspring. The 'entering plant' (E) always crosses the boundary, as the offspring is subsidized at the expense of the parent. In addition to these two extreme scenarios, an intermediate mixed strategy (M) will also be tested. The model is used to compare the efficiency of foraging in various habitats in which the proportion of resource-rich areas (p) is varied. METHODS: A stochastic cellular automata (CA) model is developed in which habitat space is represented by a honeycomb lattice. Each cell within the lattice can accommodate a single ramet, and colonization can occur from a parent ramet's cell into six neighbouring cells. The CA consists of two layers: the population layer and the habitat. In the population layer, a cell can be empty or occupied by a ramet; in the habitat layer, a cell can be good (resource-rich) or bad (resource-poor). The habitat layer is constant; the population layer changes over time, according to the birth and death of ramets. KEY RESULTS: Strategies M and E are primarily limited by patch distance, whereas A is more sensitive to patch size. At a critical threshold of the proportion of resource-rich areas, p = 0·5, the mean patch size increases abruptly. Below the threshold, E is more efficient than A, whilst above the threshold the opposite is true. The mixed strategy (M) is more efficient than either of the pure strategies across a broad range of p values. CONCLUSIONS: The model predicts more species/genotypes with the 'entering' strategy, E, in habitats where resource-rich patches are scattered, and more plants with the 'avoiding' strategy, A, in habitats where the connectivity of resource-rich patches is high. The results suggest that the degree of physiological integration between a parent and an offspring ramet is important even across a very short distance because it can strongly influence the efficiency of foraging.